(141d) DNA Collisions with Polarizable Posts

We have studied electrophoretic collisions of DNA with an ideally polarizable post. By ideally polarizable, we mean that the dielectric constant of the post ε_p is much greater than that of the surrounding fluid ε_f (i.e., ε_p>>ε_f). This situation is very different from previously studied post collision problems that either neglected the field disturbances due to the obstacle [1-2] (ε_p=ε_f) or only considered the insulating case [3] (ε_pf). For an insulating post, the electric field lines all move around the post which tends to hinder significant polymer collision events except in the case of a molecule approaching the post along the centerline. Polarizable posts, on the other hand, attract and focus the field lines which should lead to strong polymer/post interactions.

Molecular collisions with obstacles have attracted a great deal of interest recently due to their potential use in macromolecular separations [4]. In the case of DNA, collisions often lead to hooking events where a molecule drapes itself around a post with an arm stretched around each side of the post. The molecule then unhooks by one of the arms growing at the expense of the other. The time required for this unhooking process is length dependent which provides a separation mechanism that has been exploited using large post arrays. DNA separation has been demonstrated in both experiments [4] and simulations [5, 6].

More broadly speaking, molecular collisions are important because they provide a simple and convenient way to manipulate individual molecules in both applications and studies relating to fundamental science. For example, obstacle collisions have been exploited in DNA mapping devices to ?precondition? molecules for stretching in an elongational field to overcome the effects of molecular individualism [7]. And, more fundamentally, obstacles have been used to deform DNA to study the relaxation process of polymers in confined environments [8].

The electric field around an ideally polarizable post has no tangential component at the post surface, so the field lines intersect the post at right angles. On the upstream side of the post, the field lines point into the post while on the downstream side they point away. As a molecule approaches, it is driven into the post, which it cannot penetrate. Due to the finite size of the molecule (i.e., its center of mass is located slightly off the post surface), the field does provide a weak tangential component to move it around to the downstream side. Therefore, the molecule should only slowly move around the post's surface until it crosses to the downstream side where the field lines begin to emanate from the post. The downstream field can then pull the rest of the molecule around the post, at which point it can freely convect away.

When the molecule is driven into the post on the upstream side, it is compressed causing the molecule's radial dimension R_p to decrease. This length determines the molecule's exposure to the tangential field that exists off the surface of the post, and thus, it also governs the speed at which the molecule moves around the post. Based on this insight, we have developed scalings for the field-driven compression of a molecule against a solid surface, which lead to scalings for the time a molecule requires to clear a post.

We used blob theory to derive our scalings for R_p. Based on this framework, we were able to balance the entropic and enthalpic penalties due to compression against the resulting reduction of the molecule's electrical potential. Finally, we have also performed Brownian dynamics simulations in order to validate our models and more fully understand the behavior of the molecular collisions.

References:

[1] G. I. Nixon and G. W. Slater, Phys. Rev. E, 50, 5033 (1994).

[2] P. M. Saville and E. M. Sevick, Macromolecules, 32, 892 (1999).

[3] G. C. Randall and P. S. Doyle, Phys. Rev. Lett., 93, 058102 (2004).

[4] P. S. Doyle, J. Bibette, A. Bancaud, and J. L. Viovy, Science, 295, 227 (2002).

[5] P. D. Patel and E. S. G. Shaqfeh, J. Chem. Phys., 118, 2941 (2003).

[6] A. Mohan and P. S. Doyle, Phys. Rev. E, 76, 040903 (2007).

[7] A. Balducci and P. S. Doyle, Macromolecules, 41, 5485 (2008).

[8] W. D. Volkmuth, T. Duke, M. C. Wu, R. H. Austin, and A. Szabo, Phys. Rev. Lett., 72, 2117 (1994).